Lazy CrossLink Removal LCR for Geographic Routing

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Lazy Cross-Link Removal (LCR) for Geographic
Routing

• Young-Jin Kim

Co-authors Ramesh Govindan (USC)
Brad Karp (UCL)
Scott Shenker (UCB/ICSI)
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Geographic Routing
Highly scalable routing for wireless networks
Routing table size O(d) per node, d is
number of single-hop neighbors
Kim et al.,NSDI05 Frey et al., MobiCom06
LCR!!
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Greedy Forwarding
Geographic algorithms like GFG, GPSR, and GOAFR
combine greedy forwarding with face
forwarding.
G.G. Finn 87
Forwards packets to its neighbor closest to D

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Greedy forwarding may fail
x is a local minimum to D w and y are far from D
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Geographic Face Routing

• Given a radio graph, make a connected sub-graph
  without cross-links (planar graph).

Perform face traversal on planar sub-graph using
the right-hand rule and the face-change rule.
D
F4
face-change
F3
F2
right-hand rule
F1
X
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Graph Planarization

• Relative Neighborhood Graph (RNG) Toussaint,
  80 and Gabriel Graph (GG) Gabriel, 69
  long-known planar graphs
• Assume unit-disk radio model and accurate
  localization

w
u
v
?
GG
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Pitfalls of graph planarization
It does not work in real world ! Kim et al.,
NSDI05
Cross-link
68.2 routing success among node pairs !
Unidirectional
Disconnected
Wireless Network Graph from UCB Soda Hall
GG sub-graph
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Proactive Cross-Link Removal

• Cross-Link Detection Protocol (CLDP) Kim et al.,
  NSDI05 a completely distributed protocol,
  each node probes its all links to determine
  crossed links.
• No assumptions about radio model or accuracy of
  localization

pcrossings of (S, A)?
B
A
p(B, C) crosses (S, A)!
Proven that, when CLDP executes on any arbitrary
graph, it generates the sub-graph where face
traversal never fails.
pcrossings of (S, A)?
C
S
p(B, C) crosses (S, A)!
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CLDP Performance
GDSTR is better than CLDP

• GDSTR (Greedy Distributed Spanning Tree Routing)
• build Hull Tree based on locations, instead of
  planarization Leong et al., NSDI06

• But CLDP has high overhead
• - probe messages have to walk entire face

Does there exist a low overhead, yet correct,
face routing technique?
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Lazy Cross-Link Removal (LCR)
Basic Idea

• Proactively apply a graph planarization technique
  like GG (with the Mutual Witness extension).
• When a packet traversal loops,

trigger a CLDP probe on either the
looped face or adjacent faces to lazily remove
cross-link.
L
M
N
J
K
D
trigger CLDP
S
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LCR has Very Low Overhead
Lazy cross-link removal is invoked infrequently.

• GG/MW removes many, but not all, of cross-links.
• Greedy forwarding can hide some cross-links.
• Only special cross-link configurations cause
  loops.

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GG with Mutual Witness (GG/MW)

• Key idea
• remove a link only if both ends of the link see a
  mutual witness.

w
GG/MW sub-graph
v
u
?
In real-radio graphs, GG/MW removes most
cross-links, but not all.
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Fallback-to-Greedy
Many geographic face routing protocols revert to
greedy mode when sufficient forward progress is
made. This behavior can hide cross-links.
L
M
L
M
fallback to greedy
N
N
J
K
K
J
D
D
S
S
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LICL (Loop Inducing Cross-Links)

• A special condition must hold if a link crossing
  causes a loop,
• removal of both cross-links must partition the
  network graph.

L
L
M
M
N
N
K
J
J
K
D
D
S
S
LICL (Loop Inducing Cross-Link)
Cross-link does not cause loop
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Frequency of LICLs
LICLs are extremely rare in radio graphs.
LCR is invoked, on average, for only 1
cross-link!
This result not described in paper
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Details Invisible LICLs
Invisible LICL cant be detected on the looped
face.
M
S
L
M
D
N
?i
?i
L
K
J
K
D
S
Visible LICL on the walked face
Invisible LICL on the walked face
Detecting an invisible LICL a looped walk with
invisible LICL traverses the inside or outside
face of a simple polygon.
n
? ?i ((n-2)? ? ? (n2)?)
Removing the invisible LICL recursively search
adjacent faces.
Details in the paper
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Routing to Arbitrary Locations
LCR cant support data-centric storage
Cannot disambiguate between cross-links and a
destination not on the graph.
M
S
M
S
D
D
L
K
L
K
loop caused by cross-links
loop caused by destination not on the graph
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• Experimental Results Simulation
• Radio graphs with obstacles
• Radio graphs with location errors
• Compare LCR with GDSTR and CLDP
• Metric
• Overhead average number of messages per node
• Hop Stretch

• TOSSIM
• N 400 nodes

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Overhead
N/2 obstacles
LCR shows extremely low message cost
2 orders of magnitude lower than GDSTR.
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Overhead
Location Error 30 of radio range
Even in with location errors, LCR has low
overhead at high enough densities, it
incurs zero overhead.
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Overhead
Function of density, N/2, N/4, and N/8 obstacles
LCR message cost decreases in less heavily
obstructed graphs almost negligible cost in
graphs with N/8 obstacles.
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Overhead
For dynamic network, N/2 obstacles, 80 node
joins/leaves
Interestingly, GDSTR incurs overhead comparable
to the case where all nodes start at the same
time.
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Hop Stretch
Radio graphs with 30 location error
LCR suffers from high stretch at low
densities, as all face routing protocols do.
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Why?
? Geographic routing uses only local information
to determine paths. ? Deterministically
applying the right-hand or left-hand rule can
result in pathological outer perimeter walks,
increasing hop stretch.
Recently, we have discovered a technique that
can improve stretch performance.
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Intelligent Face Routing
Each local minimum learns whether to use right or
left hand rule.
This exhibits the best average stretch among face
routing protocols, comparable to GDSTR.
Recent result not described in paper
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Experimental Results
USC Tutornet 4th floor consisting of 56 Tmote sky
motes
Overhead
A Pathological LICL with many cross-links, a rare
configuration.
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Conclusion

• Instead of proactive planarization, LCR lazily
  removes
• just LICLs after they are detected.
• LCR exhibits extremely low message cost as LICLs
  are
• extremely rare in radio graphs.
• With a recent modification, LCR stretch at low
• densities compares well with competing
  proposals.

http//enl.usc.edu/projects/gpsr